Will a bearded dragon make a whole room smell?

No, Bearded Dragons themselves do not smell bad. Bearded Dragon feaces do smell however and that's why they need to be removed from the tank straight away. Depending what your Bearded Dragon eats can also affect the feaces smell. For example cockroaches or woodies smell worse than when they eat crickets.

It's not an over powering smell and it doesn't smell straight away, only if the feaces isn't removed and the tank is not regularly cleaned and sand replaced.